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Characterizing local rings via homological dimensions and regular sequences

Shokrollah Salarian·Sean Sather-Wagstaff·Siamak Yassemi
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Abstract

Let (R,m) be a Noetherian local ring of depth d and C a semidualizing R-complex. Let M be a finite R-module and t an integer between 0 and d. If G_C-dimension of M/IM is finite for all ideals I generated by an R-regular sequence of length at most d-t then either G_C-dimension of M is at most t or C is a dualizing complex. Analogous results for other homological dimensions are also given.

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Shokrollah Salarian, Sean Sather-Wagstaff, Siamak Yassemi. 2005-08-02. Characterizing local rings via homological dimensions and regular sequences. https://arxiv.org/abs/math/0401031

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